What the message looks like
452 4.2.2 Recipient address rejected: User over quota452 4.2.2 Mailbox full452-4.2.2 The recipient's inbox is out of storage space452 4.2.2 Recipient address rejected: Recipient mailbox quota exceeded
What it means
The recipient's mailbox is full or over a limit, but the receiving server is asking the sender to try again later instead of bouncing the email. The standard name for this status is "mailbox full".
Because it's temporary, the sending server keeps the email in its queue and retries. Most servers keep trying for somewhere between one and five days before giving up and sending a bounce.
If you're the recipient
Free up space, or deal with whatever limit you've hit, as soon as you can. Any email still being retried will then be delivered on the next attempt. Once the sender's server gives up, that email won't arrive, and the sender has to send it again.
If you're the sender
You don't need to do anything yet, as your server is retrying automatically. If it eventually bounces, contact the person another way to let them know their mailbox is full.
If you use addy.io
addy.io sends 452 4.2.2 Recipient address rejected: User over quota when an account on the Lite plan has gone over its monthly bandwidth limit after using its free reset for the year. Senders keep retrying while addy.io defers the email.
Wait for the next calendar month, reset your bandwidth from your subscription page or upgrade to Pro, and any email still being retried can then be delivered. See What happens if I go over my bandwidth limit.